A.E. Gelfand and A.F.M. Smith. Sampling-Based Approaches to Calculating Marginal Densities. Journal of the American Statistical Association, 85(410):398--409, 1990. Home/Search Document Not in Database Summary Related Articles Check |
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Rates of Convergence for Data Augmentation on Finite Sample Spaces - Rosenthal (1993) (3 citations) (Correct)
....posterior does not grow too quickly with the amount of observed data. This suggests the feasibility of running this iterative process when given a large but nite amount of data. In [R] similar results are obtained for a more complicated model, namely the variance component models as discussed in [GS]. The plan of this paper is as follows. In Section 2 we review the de nition of the Data Augmentation algorithm, and state the key lemma to be used in proving convergence results. In Section 3 we prove the convergence result for the case of coin tossing (i.e. when X i and Y i only take values 0 ....
....where x stands for the possible values (x n ) 2 X , y stands for the observed data (Y 1 ; Y n ) and B ( j x) means the posterior distribution on M 1 (M 1 (X ) conditional on the observations x and relative to the prior . The following Proposition is from [TW] See also [GS] for a survey of the relevant literature. We include a proof for completeness. Proposition 1. The above description de nes a time homogeneous Markov chain on M 1 (X ) with stationary distribution given by , the posterior distribution of G conditional on the observed data y = Y 1 ; Y ....
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A.E. Gelfand and A.F.M. Smith (1990), Sampling-based approaches to calculating marginal densities, J. Amer. Stat. Soc. 85, 398-409.
Random Rotations: Characters and Random Walks on SO(N) - Rosenthal (1994) (Correct)
.... This question has been motivated by such diverse areas as card shuffling ( How many times do you have to shuffle a deck of cards to make it random ; see [D] for background) and stochastic algorithms ( How long do you have to run the algorithm until the answers are satisfactory ; see e.g. [GS] and [R] In each case, it is desired to know how long a Markov chain should be run until it has converged to the desired stationary distribution. The study of non asymptotic convergence rates often yields interesting results. The best known of these is the cut off phenomonon of Diaconis and ....
A.E. Gelfand and A.F.M. Smith (1990), Sampling-based approaches to calculating marginal densities, J. Amer. Stat. Soc. 85, 398-409.
Rates of Convergence for Gibbs Sampling for Variance Component.. - Rosenthal (1991) (5 citations) (Correct)
....(MSC) Primary 62M05, secondary 60J05. 1. Introduction. In the past several years there has been a lot of attention given to the Gibbs Sampler algorithm for sampling from posterior distributions. This Markov chain Monte Carlo algorithm, popularized by Geman and Geman [GG] and summarized in [GS], has its roots in the Metropolis Hastings algorithm ( MRRTT] H] It is closely related to the Data Augmentation algorithm of Tanner and Wong [TW] It exploits the simplicity of certain conditional distributions to de ne a Markov chain that converges in law to the posterior distribution under ....
....rates are obtained for Data Augmentation for a two step hierarchical model involving Bernoulli random variables. Also, see [AKP] for an interesting analysis of a related discretization algorithm. In this paper we analyze the convergence rate of the variance component models as described in [GS], Section 3.4, and de ned herein in Section 3. See also [BT] and [GHRS] Brie y, this model involves an overall location parameter , and K di erent parameters 1 ; K which are normally distributed around . For each i there are J di erent observations Y i1 ; Y iJ , ....
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A.E. Gelfand and A.F.M. Smith (1990), Sampling-based approaches to calculating marginal densities, J. Amer. Stat. Soc. 85, 398-409.
Parallel computing and Monte Carlo algorithms - Rosenthal (1999) (1 citation) (Correct)
....computers might run at di erent speeds; they might have di erent user loads on them; one or more of them might be down; etc. Handling these issues correctly is crucial to the success of parallel Monte Carlo. In addition, Markov chain Monte Carlo algorithms are now very common (see for example [17], 51] 53] 22] 45] and parallelising them presents additional diculties such as determining appropriate burn in time. We note that similar issues have been considered in various contexts in the operations research literature. In particular, in an excellent series of papers ( 23] 24] ....
....n j is allowed to depend on the speed at which the simulation happens to run, then it follows that a second run would not produce identical results even if started with the same pseudo random number seed. 4. Parallel Markov chain Monte Carlo. Markov chain Monte Carlo (MCMC) algorithms (see e.g. [17], 51] 53] 22] 45] such as the Gibbs sampler and the Metropolis Hastings algorithm, have become extremely popular in statistics (especially Bayesian statistics) as a method of approximately computing dicult high dimensional integrals. They are also used in theoretical computer science for ....
A.E. Gelfand and A.F.M. Smith (1990), Sampling based approaches to calculating marginal densities. J. Amer. Stat. Assoc. 85, 398-409.
Tracking Multiple Objects with Particle Filtering - Hue, Le Cadre (2000) (13 citations) (Correct)
....algorithm is quite different in its principle. The vectors Xt, Kt and rt are considered to be random variables with prior densities. Samples are then obtained iteratively from their joint posterior using a proper MCMC technique, namely the Gibbs Sampler. This method has been studied in [32], 33] 34] 35] or [36] for instance. It can be run sequentially at each time period. Gibbs Sampler is a special case of the Metropolis Hasting algorithm with the proposal densities being the conditional distributions, and the acceptance probability being consequently always equal to one. The ....
A. E. Gelfand and A. F. M. Smith. Sampling-based approaches to calculating marginal densities. Journal of the American Statistical Association, 85:398-409, 1990.
Cycle-Cutset sampling for Bayesian networks - Bidyuk, Dechter (2003) (Correct)
....variables constitute a cycle cutset for the Bayesian network and otherwise it is exponential in the induced width of the network s graph, whose sampled variables are removed. Cutset sampling is an instance of the well known Rao Blakwellisation technique for variance reduction investigated in [5, 2, 16]. Moreover, the proposed scheme extends standard sampling methods to non ergodic networks with ergodic subspaces. Our empirical results con rm those expectations and show that cycle cutset sampling is superior to Gibbs sampling for a variety of benchmarks, yielding a simple, yet powerful ....
....paper, we present a sampling scheme for Bayesian networks that addresses both of these limitations by sampling from a subset of the variables. It is rooted in the well established Rao Blakwellisation methodology for sampling that was developed in the past years by various authors, most notably [5, 2, 16]. Based on the Rao Blackwell theorem ( 8] it is easy to show that sampling from a subspace (if feasible computationally) can reduce the variance and therefore yield faster convergence to the target function. The basic Rao Blackwellisation scheme can be described as follows. Suppose we partition ....
A. E. Gelfand and A. F. M. Smith. Sampling-based approaches to calculating marginal densities. Journal of the American Statistical Association, 85:398-409, 1990.
Shrinkage Estimator Generalizations of Proximal Support Vector.. - Agarwal (2002) (2 citations) (Correct)
....for all values of k. 2.5 Bayesian estimate Finally, it is possible to get a Bayesian estimate by putting a prior on and carrying out the estimation process us ing Markov Chain Monte Carlo (MCMC) algorithms. The MCMC algorithm most commonly used in statistics is Gibbs sampling, popularized by [15]. Such an approach can easily incorporate richer shrinkage strategies as discussed earlier in Section 2. However, MCMC algorithms are iterative in nature and it may be hard to scale them up to massive data mining tasks. With linear kernels, the complexity of MCMC depends mainly on n (the number of ....
A. Gelfand and A. Smith. Sampling based approaches to calculating marginal densities. Journal of the American Statistical Association, 85:398 409, 1990.
Pictorial Structures for Object Recognition - Felzenszwalb, Huttenlocher (2003) (8 citations) (Correct)
....posterior is high, and select one or more of those as correct using an independent method. This procedure lets us use somewhat inaccurate models for generating hypothesis and can be seen as a mechanism for visual selection (see [2] It is also similar to the idea behind importance sampling (see [17]) 4 1.3 E#cient Algorithms Our goal is not only to construct a framework that is rich enough to capture the appearance of many generic objects, but also to be able to e#ciently solve the object detection and model learning problems. We present such algorithms for detecting and learning a ....
A.E. Gelfand and A.F.M. Smith. Sampling-based approaches to calculating marginal densities. J. Royal Stat. Association, 85:398--409, 1990.
A Particle Filtering Approach to FM-Band Passive Radar.. - Herman, Moulin (2002) (2 citations) (Correct)
....an additional component in our measurement vector. Unfortunately, we will show in Section 2 that this is not practical with a Kalman filter (or an extended Kalman filter, for that matter) Instead, we resort to the samplebased nonparametric density estimation technique known as particle filtering [1, 2]. In addition to permitting the use of RCS as a component of our measurement vector, we will show that particle filtering also presents a useful framework for a joint approach to tracking and classification. A particle filtering approach could also be used for joint tracking and classification in ....
....approaches to density estimation. This motivation will lead us to the weighted bootstrap and its use for recursive Bayesian inference. Recursive Bayesian Inference via Weighted Bootstrap Sampling based approaches to density estimation are discussed extensively in the statistics literature [1, 2, 29, 30]. We can motivate these approaches by considering the posterior density. In the non recursive case, Bayes rule yields ( 2 # , 52) Thus, evaluation of the posterior requires knowledge of both the prior and the likelihood function , in addition to an integration to find ....
A. E. Gelfand and A. F. M. Smith, "Sampling-based approaches to calculating marginal densities," Journal of the American Statistical Association, vol. 85, pp. 398--409, June 1990.
Image Sequence Restoration Using Gibbs Distributions - Morris (1995) (13 citations) (Correct)
....with N=2 degrees of freedom [86] Thus all three conditionals may be sampled easily to generate samples from the joint distribution p(m; c; oejd) using the Gibbs sampler. From these samples there are a number of methods that can be used to obtain estimates of the marginal distributions [29]. Clearly a histogram estimate may be formed simply by plotting the histogram of each variable separately. A pointwise estimate of the marginal distribution may be formed by averaging the distributions found for each of the samples. Here we present results using the first of these two methods. ....
A.E. Gelfand and A.F.M. Smith. Sampling-based approaches to calculating marginal densities. J. American Statistical Association, 85:398--409, 1990.
Multi Sensor Management - First Year Report (Correct)
....U [0; 1] A x otherwise (2.27) The choice of the proposal distribution, T x , is a crucial step in the design process. The approach described to this point is the Metropolis Hastings algorithm. Di erent proposal distributions lead to di erent algorithms, such as the Gibbs sampler [20] and Simulated Annealing algorithm [29] One further complication arises if the proposal density can propose di erent dimensional states. In such cases, the proposal density needs to be designed with care. This jumping between di erent dimensional state spaces is Reversible Jump MCMC. The care is ....
A E Gelfand and A F M Smith. Sampling-based approaches to calculating marginal densities. In Journal of the American Statistical Association, volume 85, pages 398-409, 1990.
Approximate Nonlinear Filtering and its Application in.. - Azimi-Sadjadi And.. (2001) (3 citations) (Correct)
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A.E. Gelfand and A.F.M. Smith. Sampling-Based Approaches to Calculating Marginal Densities. Journal of the American Statistical Association, 85(410):398--409, 1990.
Approximate Nonlinear Filtering and Its Applications for.. - Azimi-Sadjadi And.. (2000) (3 citations) (Correct)
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A.E. Gelfand and A.F.M. Smith. Sampling-Based Approaches to Calculating Marginal Densities. Journal of the American Statistical Association, 85(410):398--409, 1990.
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A.E. Gelfand and A.F.M. Smith. SamplingBased Approaches to Calculating Marginal Densities. 85(410):398--409, 1990.
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Gelfand, A. and Smith, A. (1990). Sampling based approaches to calculating marginal densities. J. American Statistical Association, 85:398--409.
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Gelfand, A. and Smith, A.F.M. (1990). Sampling-based approaches to calculating marginal densities. Journal of the American Statistical Association, 85 398-409.
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Gelfand, A. E. & Smith, A. F. M. (1990), `Sampling-based approaches to calculating marginal densities', Journal of the American Statistical Association 85, 398--409.
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A. E. Gelfand and A. F. M. Smith. Sampling-based approaches to calculating marginal densities. Journal of the American Statistical Association, 85:398--409, 1990.
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GELFAND,A.E.AND SMITH,A.F.M.(1990). Sampling-based approaches to calculating marginal densities. Journal of the American Statistical Association 85, 398--409.
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Gelfand, A. E. and Smith, A. F. M. (1990). Sampling-based approaches to calculating marginal densities. Journal of the American Statistical Association 85, 398--409.
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A. E. Gelfand and A. F. M. Smith, "Sampling-based approaches to calculating marginal densities," J. Amer. Statist. Assoc., vol. 85, pp. 398--409, 1990.
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Gelfand, A.E., Smith, A.F.M.: Sampling-based approaches to calculating marginal densities. Journal of the American Statistical Association 87 (1990) 398--409
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A. E. Gelfand and A. F. M Smith. Sampling based approaches to calculating marginal densities. Journal of the American Statistical Association, 85:398--409, 1990. 13
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Gelfand, A., Smith, A.: Sampling-based approaches to calculating marginal densities. J. Am. Statistical Association 85 (1990) 398--409
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Gelfand, A. E.; Smith, A. F. M. "Sampling based approaches to calculating marginal densities". Journal of the American Statistical Association, 1990, 85, 398-409.
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A. Gelfand and A. Smith. Sampling-based approaches to calculating marginal densities. Journal of the American Statistical Association, 85(410):398--409, June 1990.
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Gelfand, A.E., Smith, A.F.M.: Sampling-Based Approaches to Calculating Marginal Densities. Journal of American Statistical Association, 85 (1990), 398-- 409
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A.E. Gelfand and A.F.M. Smith (1990), Sampling based approaches to calculating marginal densities. J. Amer. Stat. Assoc. 85, 398-409.
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A. E. Gelfand and A. F. M. Smith, "Sampling-based approaches to calculating marginal densities," J. Amer. Statist. Assoc., vol. 85, pp. 398--409, 1990.
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A.E. Gelfand and A.F.M. Smith, Sampling based approaches to calculating marginal densities, J. Amer. Statist. Assoc. 85 (1990) 398-409.
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Gelfand, A. E. and Smith, A. F. M. (1990). Sampling-based approaches to calculating marginal densities. Journal of the American Statistical Association 85 398-409.
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A.E. Gelfand and A.F.M. Smith (1990), Sampling-based approaches to calculating marginal densities, J. Amer. Stat. Soc. 85, 398-409.
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Gelfand, A. E., and Smith, A. F. M. (1990). Sampling-Based Approaches to Calculating Marginal Densities. Journal of the American Statistical Association, 85, 398--409.
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Gelfand, A., and Smith, A.F.M. (1990), Sampling based approaches to calculating marginal densities, J. Amer. Statist. Assoc. 85, 398-409.
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A. E. Gelfand and A. F. M. Smith. Sampling-based approaches to calculating marginal densities. Journal of the American Statistical Association, 85:398--409, 1990.
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Gelfand, A.E. and Smith, A.F.M., 1990. Sampling-based approaches to calculating marginal densities. Journal of the American Statistical Association, 85:398-409.
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Gelfand, A.E., and Smith, A.F.M., 1990. Sampling-based approaches to calculating marginal densities, Journal of the American Statistical Association, 85(410):398-409. 20
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Gelfand, A.E., Smith, A.F.M., 1990. Sampling-based approaches to calculating marginal densities. Journal of the American Statistical Association 85, 398-409.
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Gelfand, A.E., and Smith, A.F.M. (1990), "Sampling-Based Approaches to Calculating Marginal Densities," Journal of the American Statistical Association, 85, 398-409.
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Gelfand A.E. and Smith A.F.M. (1990), Sampling based approaches to calculating marginal densities. J. Amer. Stat. Assoc. 85, 398-409.
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A. E. Gelfand and A. F. M Smith. Sampling based approaches to calcu- lating marginal densities. Journal of the American Statistical Association, 85:398-409, 1990.
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A. E. Gelfand and A. F. M Smith. Sampling based approaches to calculating marginal densities. Journal of the American Statistical Association, 85:398-409, 1990.
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A. E. Gelfand and A. F. M Smith. Sampling based approaches to calculating marginal densities. Journal of the American Statistical Association, 85:398-409, 1990.
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A. E. Gelfand and A. F. M Smith. Sampling based approaches to calculating marginal densities. Journal of the American Statistical Association, 85:398-409, 1990.
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A. E. Gelfand and A. F. M. Smith, "Sampling-based approaches to calculating marginal densities," Journal of the American Statistical Association, vol. 85,
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A. E. Gelfand and A. F. M. Smith, "Sampling-based approaches to calculating marginal densities," Journal of the American Statistical Association, vol. 85, pp. 398--409, June 1990. 127
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Gelfand A. and Smith, A.F.M. (1990) Sampling based approaches to calculating marginal densities. J. Am. Statist. Ass., 85, 398-409.
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